======================================================================= TITLE: Bayesian Nonparametric Mixture Modelling: Methods and Applications COURSE DESCRIPTION Bayesian methods are becoming an increasingly important framework for modern statistical modelling. In particular, recent research in Bayesian nonparametric and semiparametric methods has resulted in considerably expanding the flexibility of standard Bayesian models and indicated their utility in a wide variety of application fields. A two-day intensive course on the methods and practice of Bayesian modelling using nonparametric priors will be given at NUI Galway on 14th and 15th December (Monday and Tuesday), 2009. The main goal of the course will be to introduce Bayesian nonparametric methods with emphasis on nonparametric mixture models, and with a focus on practical applications. The course will provide a general introduction to nonparametric priors for spaces of random functions with a detailed account of models based on the Dirichlet process (a nonparametric prior for distribution functions) and Dirichlet process mixtures. Among the topics will be an overview of theoretical results, methodological details, and computational techniques for posterior inference. Examples will be given from a variety of settings, including density estimation, nonparametric regression, survival analysis, and spatial statistics. The lectures will use slides specially prepared for the course. These will be handed out to the participants. Some of the data illustrations will use "DPpackage", the recently released, publicly available, R package. The analysis for at least one data example will be developed during the course. Sufficient preparation for the course includes statistics training to the M.S. level and exposure to Bayesian hierarchical modelling and computation. The main presenter will be Athanasios Kottas, Associate Professor of Statistics, Department of Applied Mathematics and Statistics, University of California, Santa Cruz. The co-presenter will be Milovan Krnjajic, Stokes Lecturer in Statistics, School of Mathematics, NUI Galway. OUTLINE -- Morning Session I (Monday December 14, 11:00--13:00) Motivation for Bayesian nonparametric modeling. General approaches for construction of nonparametric priors. Dirichlet process (DP) priors and mixtures of DP priors: definitions, properties, and methods. Applications to Bayesian bio-assay (dose-response) modeling. (Break) -- Afternoon Session I (Monday December 14, 14:00--17:00) Dirichlet process mixture models: definitions, examples, methods for posterior inference and prediction. Connections with finite mixture models. (Break) -- Morning Session II (Tuesday December 15, 9:00--12:00) Applications of DP mixture models: density estimation, nonparametric curve fitting, quantile regression, survival analysis, multivariate ordinal data analysis. (Break) -- Afternoon Session II (Tuesday December 15, 14:00--17:00) Applications of DP mixture models (continued): Receiver Operating Characteristic (ROC) data analysis, inference for temporal and spatial Poisson processes. Overview of extensions of DP priors and DP mixture models: dependent DP priors, hierarchical DP mixtures, nested DP priors, spatial DP prior models. PRESENTERS Athanasios Kottas obtained a Ph.D. in Statistics from the University of Connecticut in 2000 with a dissertation on Bayesian nonparametric modelling and inference using Dirichlet process mixing. From 2000 to 2002, he was a Visiting Assistant Professor in the Institute of Statistics and Decision Sciences, Duke University. He is currently an Associate Professor in Statistics at the University of California, Santa Cruz. His research interests include Bayesian nonparametrics, mixture models, point process modelling, quantile regression, and survival analysis, with applications in ecology and engineering. He was a co-presenter for three short courses on applied Bayesian nonparametric modelling (summers of 2005, 2006, and 2009), and the instructor of four regular courses on Bayesian nonparametrics at Duke University and at University of California, Santa Cruz. He is Associate Editor for journal Bayesian Analysis, has published 30 papers, has served as advisor/co-advisor for two Ph.D. dissertations, and is currently supervising three Ph.D. students. Milovan Krnjajic obtained a Ph.D. in Statistics from the University of California at Santa Cruz in 2005 with a dissertation on Bayesian Model Specification and Non-Parametric Inference. Before joining NUI Galway as a Stokes Lecturer in Statistics, his recent posts were as a risk analyst at Merrill Lynch, New York, and a senior researcher at the Lawrence Livermore National Laboratory, USA. He is interested in applied statistical modelling in variety of fields, in particular in the development of regression and mixture models based on Bayesian non-parametrics, inverse models, and classification methods of machine learning. Organized by John Hinde and Milovan Krnjajic. Further details about the course are available from Milovan (milovan.krnjajic@nuigalway.ie).